BANK & INSURANCE (RATIO AND PROPORTION) PART 2

Total Questions: 70

31. Sweeta is 10 years younger than her sister Seema who was 14 years old when her mother was 34 years old. The ratio of the ages of the mother and Sweeta after 6 years will be 2 : 1. After how many years the average of their ages will be 39.33 years?

Correct Answer: (b) 2 years
Solution:

Let the present age of Seema be x years

Sweeta’s present age = x − 10

When Seema was 14 years, mother was 34 years. So, when Seema is x years, mother will be = 34 − 14 + x

Mother’s present age = 20 + x

According to the question,

(x + 20 + 6) / (x − 10 + 6) = 2 / 1

(x + 26) / (x − 4) = 2

x + 26 = 2x − 8

x = 34 years

Seema’s age = 34 years

Sweeta’s age = 24 years

Mother’s present age = 54 years

Average = (34 + 24 + 54) / 3 = 37.33 years

After 2 years, Seema’s age = 36 years, Sweeta’s age = 26 years, Mother’s age = 56 years

Average after 2 years,

Avg = (36 + 26 + 56) / 3 = 39.33 years

32. The number of students in school A, B and C are in a ratio of 5 : 4 : 8 respectively. If the number of students is increased by 40%, 75% and 25% respectively in next year and the total students after increment is 1200, what was the total number of students initially?

Correct Answer: (c) 850
Solution:

Let the students in school A, B and C be 5x, 4x, 8x

After increment, students in school A = 5x × 140% = 7x

After increment, students in school B = 4x × 175% = 7x

After increment, students in school C = 8x × 125% = 10x

According to the question,

7x + 7x + 10x = 1200

24x = 1200

x = 50

Students in school A initially = 5 × 50 = 250
Students in school B initially = 4 × 50 = 200
Students in school C initially = 8 × 50 = 400

Required number of students = 250 + 200 + 400
= 850

33. Monthly salaries of A and B are in the ratio 8 : 9 respectively. Monthly expenditure of A is 140% more than the monthly savings of B. Monthly expenditure of B is Rs. 2000 more than the monthly expenditure of A. Find the difference in the yearly salaries of A and B if the monthly savings of A and B are in the ratio 4 : 5 respectively.

Correct Answer: (e) None of these
Solution:

Let the monthly savings of A and B are Rs. 4x and Rs. 5x respectively

Monthly expenditure of A = 2.40 × 5x = Rs. 12x

Monthly expenditure of B = Rs. 12x + 2000

So, monthly salary of A = Rs. (4x + 12x) = Rs. 16x

Monthly salary of B = Rs. (5x + 12x + 2000) = Rs. (17x + 2000)

So, according to the question,

(4x + 12x) / (5x + 12x + 2000) = 8 / 9

2x / (17x + 2000) = 1 / 9

18x = 17x + 2000; x = 2000

So, monthly salary of A = 16 × 2000 = Rs. 32000

Monthly salary of B = 17 × 2000 + 2000 = Rs. 36000

Difference in the monthly salaries of A and B = 36000 − 32000 = Rs. 4000

Difference in the yearly salaries of A and B = 12 × 4000 = Rs. 48000

34. In a town with population of 4500, the ratio of males to females is 3 : 2 and the ratio of females to children is 4 : x. In election of Nagar - Palika, two candidates are there, children aren’t allowed to vote and 10% of the eligible population didn’t cast their vote. If the winner candidate won by 400 votes and the runner up candidate got 1150 votes, then find the value of ‘x’.

[Note: Total population of village = Male + Female + Children]

Correct Answer: (e) 5
Solution:

Total votes got by winner and runner up = (1150 + 400) + 1150 = 2700

These 2700 votes are given by 90% of male and female as 10% of male and female did not cast their vote.

So, 90% of total male and female = 2700

So, total male + female = 3000

Therefore, number of children = 1500

Ratio of Male : Female : children = 3 : 2 : 2 : x
= 6 : 4 : x

The number of children is 1500 which is half of the total number of male and female which is 3000.

So, x will be half the number of parts of male and female in the ratio which will be equal to 5 as total part of male and female is (6 + 4 = 10)

Hence,  5 is correct.

35. 5 years ago, the age of father was 2.25 times the age of his son. 2 years hence, the age of father becomes 2.6 times the age of his daughter. If the son is 7 years elder to daughter, the present age of Father.

Correct Answer: (d) 50 years
Solution:

Let the present age of father, son and daughter be F, S and D respectively.

According to the question,

5 years ago, the age of father is 2.25 times the age of son.

F − 5 = 2.25 (S − 5)

F = 2.25S − 5 (2.25 − 1)

F = 2.25S − 6.25 ...(1)

2 years hence, the age of father becomes 2.6 times the age of daughter.

F = 2.6D + 2 (2.6 − 1)

F = 2.6D + 3.2 ...(2)

S − D = 7 ...(3)

From (1) and (2),

2.25S − 6.25 = 2.6D + 3.2

2.25S − 2.6D = 9.45 ...(4)

Multiply (3) by 2.25 and subtract it from (4)

−0.35D = −6.3

D = 18 years, S = 18 + 7 = 25 years

Substitute value of D in (2),

F = 2.6 × 18 + 3.2

F = 50 years

36. Number of students in Arts and science faculties in an institute are in the ratio of 5 : 8 respectively. If 150 more students join arts faculty, while 80 more students join science faculty, the respective ratio becomes 3 : 4. Originally what was the total number of students in both faculties together?

Correct Answer: (e) None of these
Solution:

Let the original number of students in arts and science faculties be 5x and 8x respectively.

According to the question,

(x + 150) / (8x + 80) = 3 / 4

24x + 240 = 20x + 600

4x = 360

⇒ x = 90

Original number of students = 5x + 8x = 13x
= 13 × 90 = 1170

37. An amount of money is divided among P, Q and R in ratio of 3 : 5 : 7, respectively. If the amount received by R is Rs. 4000 more than the amount received by Q, what will be the total amount received by P and Q together?

Correct Answer: (c) Rs. 16000
Solution:

Ratio = 3 : 5 : 7 = 3x : 5x : 7x

R = 4000 + Q

R − Q = 4000

X(7 − 5) = 4000

X = 2000

P = 3 × 2000 = 6000

Q = 5 × 2000 = 10000

R = 7 × 2000 = 14000

Total amount received by P and Q = 6000 + 10000 = Rs. 16000

38. A sum of money is divided among A, B, C and D in the ratio 2 : 3 : 7 : 11. If the share of C is Rs 2755 more than A, then the sum of money by B and D together is?

Correct Answer: (d) Rs. 7714
Solution:

Ratio of money divided among A, B, C and D is 2 : 3 : 7 : 11

Let x be the common factor in the given ratio, 2x : 3x : 7x : 11x

Difference in ratio value between C and A

⇒ 7x − 2x = 5x

Actual difference = 2755

X = 551

Ratio of B and D together = 3x + 11x = 14x

Total amount of B and D together = 14 × 551

= Rs. 7714

39. The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4 and its perimeter is 104 cm. The length of the longest side is (in cm).

Correct Answer: (c) 48
Solution:

The ratio between sides of triangle is 1/2 : 1/3 : 1/4

Let, first side /2 = second side /3 = third side /4 = x

⇒ x/2 + x/3 + x/4 = 104

⇒ 6x + 4x + 3x = 12 × 104

⇒ 13x = 12 × 104

⇒ x = 96

Longest side is x/2 = 48

40. In a company, ratio of male to female employees 7 : 3 and the monthly salary of a male employee is 60% of the total number of employees and monthly salary of a female employee is 90% salary of a male employee. If the total salary of male and female employee is Rs.5238000 then find the number of employees in the company.

Correct Answer: (a) 3000
Solution:

Total number of male and female are 7x and 3x

Salary of a male = 60% of 10x = 6x

Salary of a female = 90% Salary of a male = 90% of 6x = 5.4x

Total salary = 7x × 6x + 3x × 5.4x = 5238000

58.2(x)² = 5238000

(x)² = 90000

X = 300

Total employees = 10x = 10 × 300 = 3000